Journal of Mathematical Chemistry
, Volume 2, Issue 3, pp 267277
First online:
How to compute the Wiener index of a graph
 Bojan MoharAffiliated withDepartment of Ma theima tics, University E.K. of LjubljanaDepartment of Mathematics and Statistics, Simon Fraser University
 , Tomaž PisanskiAffiliated withDepartment of Ma theima tics, University E.K. of LjubljanaDepartment of Mathematics and Statistics, Simon Fraser University
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The Wiener index of a graphG is equal to the sum of distances between all pairs of vertices ofG. It is known that the Wiener index of a molecular graph correlates with certain physical and chemical properties of a molecule. In the mathematical literature, many good algorithms can be found to compute the distances in a graph, and these can easily be adapted for the calculation of the Wiener index. An algorithm that calculates the Wiener index of a tree in linear time is given. It improves an algorithm of Canfield, Robinson and Rouvray. The question remains: is there an algorithm for general graphs that would calculate the Wiener index without calculating the distance matrix? Another algorithm that calculates this index for an arbitrary graph is given.
 Title
 How to compute the Wiener index of a graph
 Journal

Journal of Mathematical Chemistry
Volume 2, Issue 3 , pp 267277
 Cover Date
 198807
 DOI
 10.1007/BF01167206
 Print ISSN
 02599791
 Online ISSN
 15728897
 Publisher
 Kluwer Academic Publishers
 Additional Links
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 Industry Sectors
 Authors

 Bojan Mohar ^{(1)} ^{(2)}
 Tomaž Pisanski ^{(1)} ^{(2)}
 Author Affiliations

 1. Department of Ma theima tics, University E.K. of Ljubljana, Jadranska 19, 61111, Ljubljana, Yugoslavia
 2. Department of Mathematics and Statistics, Simon Fraser University, Burnaby, B. C., Canada